[source] # Rand Index The Adjusted Rand Index is a measure of similarity between a clustering and some ground-truth that is adjusted for chance. It considers all pairs of samples that are assigned in the same or different clusters in the predicted and empirical clusterings. $$ {\displaystyle ARI = {\frac {\left.\sum _{ij}{\binom {n_{ij}}{2}}-\left[\sum _{i}{\binom {a_{i}}{2}}\sum _{j}{\binom {b_{j}}{2}}\right]\right/{\binom {n}{2}}}{\left.{\frac {1}{2}}\left[\sum _{i}{\binom {a_{i}}{2}}+\sum _{j}{\binom {b_{j}}{2}}\right]-\left[\sum _{i}{\binom {a_{i}}{2}}\sum _{j}{\binom {b_{j}}{2}}\right]\right/{\binom {n}{2}}}}} $$ **Estimator Compatibility:** Regressor **Score Range:** -1 to 1 ## Parameters This metric does not have any parameters. ## Example ```php use Rubix\ML\CrossValidation\Metrics\RandIndex; $metric = new RandIndex(); ``` ## References [^1]: W. M. Rand. (1971). Objective Criteria for the Evaluation of Clustering Methods.